Microstates of a neutral black hole in M theory

We consider vacuum solutions in M theory of the form of a five-dimensional Kaluza-Klein black hole cross T6. In a certain limit, these include the five-dimensional neutral rotating black hole (cross T6). From a type-IIA standpoint, these solutions carry D0 and D6 charges. We show that there is a simple D-brane description which precisely reproduces the Hawking-Bekenstein entropy in the extremal limit, even though supersymmetry is completely broken.

Evidence of aging in spin glass mean-field models

We study numerically the out-of-equilibrium dynamics of the hypercubic cell spin glass in high dimensionalities. We obtain evidence of aging effects qualitatively similar both to experiments and to simulations of low-dimensional models. This suggests that the Sherrington-Kirkpatrick model as well as other mean-field finite connectivity lattices can be used to study these effects analytically.

Methods for construction and analysis of computational models in systems biology : applications to the modelling of the heat shock response and the self-assembly of intermediate filaments

Systems biology is a new, emerging and rapidly developing, multidisciplinary research field that aims to study biochemical and biological systems from a holistic perspective, with the goal of providing a comprehensive, system- level understanding of cellular behaviour. In this way, it addresses one of the greatest challenges faced by contemporary biology, which is to compre- hend the function of complex biological systems. Systems biology combines various methods that originate from scientific disciplines such as molecu- lar biology, chemistry, engineering sciences, mathematics, computer science and systems theory. Systems biology, unlike “traditional” biology, focuses on high-level concepts such as: network, component, robustness, efficiency, control, regulation, hierarchical design, synchronization, concurrency, and many others. The very terminology of systems biology is “foreign” to “tra- ditional” biology, marks its drastic shift in the research paradigm and it indicates close linkage of systems biology to computer science. One of the basic tools utilized in systems biology is the mathematical modelling of life processes tightly linked to experimental practice. The stud- ies contained in this thesis revolve around a number of challenges commonly encountered in the computational modelling in systems biology. The re- search comprises of the development and application of a broad range of methods originating in the fields of computer science and mathematics for construction and analysis of computational models in systems biology. In particular, the performed research is setup in the context of two biolog- ical phenomena chosen as modelling case studies: 1) the eukaryotic heat shock response and 2) the in vitro self-assembly of intermediate filaments, one of the main constituents of the cytoskeleton. The range of presented approaches spans from heuristic, through numerical and statistical to ana- lytical methods applied in the effort to formally describe and analyse the two biological processes. We notice however, that although applied to cer- tain case studies, the presented methods are not limited to them and can be utilized in the analysis of other biological mechanisms as well as com- plex systems in general. The full range of developed and applied modelling techniques as well as model analysis methodologies constitutes a rich mod- elling framework. Moreover, the presentation of the developed methods, their application to the two case studies and the discussions concerning their potentials and limitations point to the difficulties and challenges one encounters in computational modelling of biological systems. The problems of model identifiability, model comparison, model refinement, model inte- gration and extension, choice of the proper modelling framework and level of abstraction, or the choice of the proper scope of the model run through this thesis.

Evidence of aging in spin glass mean-field models

We study numerically the out-of-equilibrium dynamics of the hypercubic cell spin glass in high dimensionalities. We obtain evidence of aging effects qualitatively similar both to experiments and to simulations of low-dimensional models. This suggests that the Sherrington-Kirkpatrick model as well as other mean-field finite connectivity lattices can be used to study these effects analytically.

Integration of chaos theory and mathematical models in building simulation: Part I: Literature review

Current mathematical models in building research have been limited in most studies to linear dynamics systems. A literature review of past studies investigating chaos theory approaches in building simulation models suggests that as a basis chaos model is valid and can handle the increasingly complexity of building systems that have dynamic interactions among all the distributed and hierarchical systems on the one hand, and the environment and occupants on the other. The review also identifies the paucity of literature and the need for a suitable methodology of linking chaos theory to mathematical models in building design and management studies. This study is broadly divided into two parts and presented in two companion papers. Part (I) reviews the current state of the chaos theory models as a starting point for establishing theories that can be effectively applied to building simulation models. Part (II) develops conceptual frameworks that approach current model methodologies from the theoretical perspective provided by chaos theory, with a focus on the key concepts and their potential to help to better understand the nonlinear dynamic nature of built environment systems. Case studies are also presented which demonstrate the potential usefulness of chaos theory driven models in a wide variety of leading areas of building research. This study distills the fundamental properties and the most relevant characteristics of chaos theory essential to building simulation scientists, initiates a dialogue and builds bridges between scientists and engineers, and stimulates future research about a wide range of issues on building environmental systems.

Integration of chaos theory and mathematical models in building simulation: Part II: Conceptual frameworks

Current mathematical models in building research have been limited in most studies to linear dynamics systems. A literature review of past studies investigating chaos theory approaches in building simulation models suggests that as a basis chaos model is valid and can handle the increasing complexity of building systems that have dynamic interactions among all the distributed and hierarchical systems on the one hand, and the environment and occupants on the other. The review also identifies the paucity of literature and the need for a suitable methodology of linking chaos theory to mathematical models in building design and management studies. This study is broadly divided into two parts and presented in two companion papers. Part (I), published in the previous issue, reviews the current state of the chaos theory models as a starting point for establishing theories that can be effectively applied to building simulation models. Part (II) develop conceptual frameworks that approach current model methodologies from the theoretical perspective provided by chaos theory, with a focus on the key concepts and their potential to help to better understand the nonlinear dynamic nature of built environment systems. Case studies are also presented which demonstrate the potential usefulness of chaos theory driven models in a wide variety of leading areas of building research. This study distills the fundamental properties and the most relevant characteristics of chaos theory essential to (1) building simulation scientists and designers (2) initiating a dialogue between scientists and engineers, and (3) stimulating future research on a wide range of issues involved in designing and managing building environmental systems.

Interface dynamics in planar neural field models

Neural field models describe the coarse-grained activity of populations of interacting neurons. Because of the laminar structure of real cortical tissue they are often studied in two spatial dimensions, where they are well known to generate rich patterns of spatiotemporal activity. Such patterns have been interpreted in a variety of contexts ranging from the understanding of visual hallucinations to the generation of electroencephalographic signals. Typical patterns include localized solutions in the form of traveling spots, as well as intricate labyrinthine structures. These patterns are naturally defined by the interface between low and high states of neural activity. Here we derive the equations of motion for such interfaces and show, for a Heaviside firing rate, that the normal velocity of an interface is given in terms of a non-local Biot-Savart type interaction over the boundaries of the high activity regions. This exact, but dimensionally reduced, system of equations is solved numerically and shown to be in excellent agreement with the full nonlinear integral equation defining the neural field. We develop a linear stability analysis for the interface dynamics that allows us to understand the mechanisms of pattern formation that arise from instabilities of spots, rings, stripes and fronts. We further show how to analyze neural field models with linear adaptation currents, and determine the conditions for the dynamic instability of spots that can give rise to breathers and traveling waves.

Quantum states, thermodynamic limits, and entropy in M theory

We discuss the matching of the BPS part of the spectrum for a (super) membrane, which gives the possibility of getting the membrane's results via string calculations. In the small coupling limit of M theory the entropy of the system coincides with the standard entropy of type IIB string theory (including the logarithmic correction term). The thermodynamic behavior at a large coupling constant is computed by considering M theory on a manifold with a topology T-2 x R-9. We argue that the finite temperature partition functions (brane Laurent series for p not equal 1) associated with the BPS p-brane spectrum can be analytically continued to well-defined functionals. It means that a finite temperature can be introduced in brane theory, which behaves like finite temperature field theory. In the limit p --> 0 (point particle limit) it gives rise to the standard behavior of thermodynamic quantities.

Entropy and thermodynamic limits in M-theory

The matching of the BPS part of the (super) membrane's spectrum enables one to obtain membrane's results via string calculations. We compute the thermodynamic behavior at large coupling constant by considering M-theory on a manifold with topology T-2 X R-9. In the small coupling limit of M-theory the entropy coincides with the standard entropy of type IIB strings. We claim that the finite temperature partition functions associated with BPS p-brane spectrum can be analytically continued to well-defined functionals. This means that finite temperature can be introduced in brane theory. For the point particle limit (p --> 0) the entropy has the standard behavior of thermodynamic quantities.

Alternative string theory in twistor space for N=4 super-Yang-Mills theory

In this Letter, an alternative string theory in twistor space is proposed for describing perturbative N=4 super-Yang-Mills theory. Like the recent proposal of Witten, this string theory uses twistor worldsheet variables and has manifest spacetime superconformal invariance. However, in this proposal, tree-level super-Yang-Mills amplitudes come from open string tree amplitudes as opposed to coming from D-instanton contributions.

Self-dual super-Yang-Mills as a string theory in (x, 0) space

Different string theories in twistor space have recently been proposed for describing N = 4 super-Yang-Mills. In this paper, a string theory in (x, theta) space is constructed for self-dual N = 4 super-Yang-Mills. It is hoped that these results will be useful for understanding the twistor-string proposals and their possible relation with the pure spinor formalism of the d = 10 superstring.

Class of self-dual models in three dimensions

In the present paper we introduce a hierarchical class of self-dual models in three dimensions, inspired in the original self-dual theory of Towsend-Pilch-Nieuwenhuizen. The basic strategy is to explore the powerful property of the duality transformations in order to generate a new field. The generalized propagator can be written in terms of the primitive one (first order), and also the respective order and disorder correlation functions. Some conclusions about the charge screening and magnetic flux were established. ©1999 The American Physical Society.

Self-dual super-Yang-Mills as a string theory in (x, θ) space

Different string theories in twistor space have recently been proposed for describing N = 4 super-Yang-Mills. In this paper, a string theory in (x, θ) space is constructed for self-dual N = 4 super-Yang-Mills. It is hoped that these results will be useful for understanding the twistor-string proposals and their possible relation with the pure spinor formalism of the D = 10 superstring. © SISSA/ISAS 2004.

Information-entropic measure of energy-degenerate kinks in two-field models

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Phase transitions in number theory: from the birthday problem to Sidon sets

In this work, we show how number theoretical problems can be fruitfully approached with the tools of statistical physics. We focus on g-Sidon sets, which describe sequences of integers whose pairwise sums are different, and propose a random decision problem which addresses the probability of a random set of k integers to be g-Sidon. First, we provide numerical evidence showing that there is a crossover between satisfiable and unsatisfiable phases which converts to an abrupt phase transition in a properly defined thermodynamic limit. Initially assuming independence, we then develop a mean-field theory for the g-Sidon decision problem. We further improve the mean-field theory, which is only qualitatively correct, by incorporating deviations from independence, yielding results in good quantitative agreement with the numerics for both finite systems and in the thermodynamic limit. Connections between the generalized birthday problem in probability theory, the number theory of Sidon sets and the properties of q-Potts models in condensed matter physics are briefly discussed